Andrea's tips

Children love to dip their food -- how about using a small muffin liner to serve their dip in. It keeps it in one place and their plate is easier for clean-up. They can also be used to separate food on a plate (perhaps a few grapes, few crackers etc.)
Keep babies happy after eating in their highchair -- add some water and some suds (with tear-free soap) to their highchair tray. Yes, it will get the floor wet (but I found it handy for doing a quick wash-up) best of all though their hands and tray get nice and clean. Water play is very stimulating for children, and babies love it.